document.write( "Question 1088065: Three presidents,3 secretaries and 3 treasurer's are to occupy 9 seats for a round table discussion about a certain issue.In how many ways can they arranged themselves if
\n" ); document.write( "1.they sit anywhere they want
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\n" ); document.write( "3.Secretaries sit together and treasurer's sit together? \n" ); document.write( "
Algebra.Com's Answer #702354 by Edwin McCravy(20056)\"\" \"About 
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Three presidents,3 secretaries and 3 treasurer's are to
\n" ); document.write( "occupy 9 seats for a round table discussion about a certain
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\n" ); document.write( "3.Secretaries sit together and treasurer's sit together?
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document.write( "[I hate round table problems (lol!) because they always make \r\n" );
document.write( "the very unrealistic assumption that the people, table and \r\n" );
document.write( "chairs were all sitting on a huge turntable, and that the \r\n" );
document.write( "huge turntable can be rotated so that regardless of how the\r\n" );
document.write( "turntable is rotated, it's the same seating arrangement.]\r\n" );
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document.write( "The best way to handle these problems is to pick one of the \r\n" );
document.write( "n people to face north,  and then seat the other n-1 people \r\n" );
document.write( "around that person.  \r\n" );
document.write( "Let's pick one of the presidents to face north, call him \r\n" );
document.write( "Mr. P.  Then we have 8 people composed of only 2 presidents, \r\n" );
document.write( "3 secretaries, and 3 treasurers to sit around Mr. P, like\r\n" );
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document.write( "     P\r\n" );
document.write( "  1     8\r\n" );
document.write( " 2       7\r\n" );
document.write( "  3     6\r\n" );
document.write( "    4 5\r\n" );
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document.write( "There are 8 positions around Mr. P.\r\n" );
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document.write( "Answer: 8! = 40320\r\n" );
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\n" ); document.write( "2.Presidents sit together?
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document.write( "We can place the 2 other presidents on Mr. P's right in 2! ways,\r\n" );
document.write( "on his left in 2!, or one on each side of him in 2! ways.  That's \r\n" );
document.write( "3*2! ways to seat the other 2 presidents.  Then we can seat the \r\n" );
document.write( "other 6 people in 6! ways.\r\n" );
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document.write( "Answer 3*2!*6! = 4320 ways\r\n" );
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\n" ); document.write( "3.Secretaries sit together and treasurer's sit together?
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document.write( "We can arrange the trio of secretaries in 3! ways.\r\n" );
document.write( "We can arranges the trio of treasurers in 3! ways.  \r\n" );
document.write( "Then we have 1 trio of secretaries, 1 trio of treasurers and 2\r\n" );
document.write( "single people (presidents) to place around Mr. P.  That's 4 \r\n" );
document.write( "\"things\" to place around Mr. P.  We can do that in 4! ways.\r\n" );
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document.write( "Answer: 3!3!4!  = 864 ways\r\n" );
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document.write( "Edwin
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